We examine the recently proposed imaginary-time formulation for strongly correlated steady-state nonequilibrium for its range of validity and discuss significant improvements in the analytic continuation of the Matsubara voltage as well as the fermionic Matsubara frequency. The discretization error in the conventional Hirsch-Fye algorithm has been compensated in the Fourier transformation with reliable small frequency behavior of self-energy. Here we give detailed discussions for generalized

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... ctral representation ansatz by including high order vertex corrections and its numerical analytic continuation procedures. The differential conductance calculations agree accurately with existing data from other nonequilibrium transport theories. It is verified that, at finite source-drain voltage, the Kondo resonance is destroyed at bias comparable to the Kondo temperature. Calculated coefficients in the scaling relation of the zero bias anomaly fall within the range of experimental estimates.